Now $h_a : Vn\rightarrow Sn_1$ where $Vn$ and $Sn_1$ is vector space representation of $GF(2^n)$ and $H_u$. To get from $GF(2^n)$ to $Vn$ and back I am good with But to create $h_2$ I have no luck. My attempts to use

Comments

The curly brackets got lost in the definition of H_u. The function $l(x)=x^(2^i)+x$ is linear over GF(2^(n+1)) and H_u is image of $l(x)$ giving that H_u is a subgroup of GF and can also be seen as a vector space.

Your first code excerpt does not work for me: on `Hom(Kn_1, H_u)` it complains that `H_u` is a list. Set morphisms forget a lot of structure about you vector spaces. Have you considered using `Kn_1.vector_space()` and working with matrices?

H_u was suppose to the a multiplicative subgroup of Kn_1 and now can't get away to generate a subgroup in sage. The reason I want to use a morphism is that I am only interested in the Range and Domain and the mapping. This will also help met to learn a functionality of sage.